Process for production of silicon single crystal, and highly doped N-type semiconductor substrate

ABSTRACT

After adding phosphorus (P) and germanium (Ge) into a silicon melt or adding phosphorus into a silicon/germanium melt, a silicon monocrystal is grown from the silicon melt by a Czochralski method, where a phosphorus concentration [P] L (atoms/cm 3 ) in the silicon melt, a Ge concentration in the silicon monocrystal, an average temperature gradient G ave  (K/mm) and a pull speed V (mm/min) are controlled to satisfy a formula (1) as follows, a phosphorus concentration [P](atoms/cm 3 ) and the Ge concentration [Ge](atoms/cm3) in the silicon monocrystal satisfy a relationship according to a formula (2) as follows while growing the silicon monocrystal, where d Si (Å) represents a lattice constant of silicon, r Si (Å) represents a covalent radius of silicon, r P (Å) represents a covalent radius of phosphorus, and r Ge (Å) represents a covalent radius of Ge: 
     
       
         
           
             
               
                 
                   
                     
                       
                         [ 
                         P 
                         ] 
                       
                       L 
                     
                     + 
                     
                       
                         ( 
                         
                           
                             0.3151 
                             × 
                             
                               [ 
                               Ge 
                               ] 
                             
                           
                           + 
                           
                             3.806 
                             × 
                             
                               10 
                               18 
                             
                           
                         
                         ) 
                       
                       / 
                       1.5 
                     
                   
                   &lt; 
                   
                     0.5 
                     × 
                     
                       ( 
                       
                         
                           
                             G 
                             ave 
                           
                           / 
                           V 
                         
                         + 
                         43 
                       
                       ) 
                     
                     × 
                     
                       10 
                       19 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             ( 
                             
                               
                                 
                                   r 
                                   Ge 
                                 
                                 - 
                                 
                                   r 
                                   Si 
                                 
                               
                               
                                 r 
                                 Si 
                               
                             
                             ) 
                           
                           × 
                           
                             
                               [ 
                               Ge 
                               ] 
                             
                             
                               [ 
                               Si 
                               ] 
                             
                           
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 
                                   r 
                                   p 
                                 
                                 - 
                                 
                                   r 
                                   Si 
                                 
                               
                               
                                 r 
                                 Si 
                               
                             
                             ) 
                           
                           × 
                           
                             
                               [ 
                               P 
                               ] 
                             
                             
                               [ 
                               Si 
                               ] 
                             
                           
                         
                       
                       ) 
                     
                     × 
                     
                       d 
                       si 
                     
                   
                   &lt; 
                   
                     
                       
                         - 
                         4.24736 
                       
                       × 
                       
                         10 
                         
                           - 
                           23 
                         
                       
                       × 
                       
                         [ 
                         P 
                         ] 
                       
                     
                     + 
                     
                       2.78516 
                       × 
                       
                         
                           10 
                           
                             - 
                             3 
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   )

This is a Divisional of U.S. application Ser. No. 12/602,479, filed Nov.30, 2009, which is a U.S. National Phase Application under 35 USC 371 ofInternational Application PCT/JP2008/059512, filed May 23, 2008.

TECHNICAL FIELD

The present invention relates to a producing method of a siliconmonocrystal and an N-type highly doped semiconductor substrate.

BACKGROUND ART

Epitaxial layers are often provided on silicon wafer substrates highlydoped with P-type or N-type dopants in order to improve performance ofsemiconductor devices.

When dopant atoms are highly doped on silicon substrates, difference inthe size (covalent radius) of the dopant atoms and silicon substrateatoms results in a strain in crystal to generate an internal stress. Themagnitude of the generated stress increases in accordance with thethickness of the epitaxial layers.

When a lowly doped epitaxial layer is provided on such a highly dopedsemiconductor substrate, misfit dislocation occurs at an interfacebetween the substrate and the epitaxial layer, which is transmitted tothe topmost surface of the epitaxial layer. The generated dislocationcauses junction leakage and the like to impair the performance of thesemiconductor devices.

It has therefore been proposed that, when boron (B) is used as P-typedopant and to be highly doped, germanium (Ge) is doped together withboron (see, for instance, Patent Documents 1 and 2).

According to Patent Document 1, the added germanium restrains decreasein lattice constant of silicon caused on account of the large amount ofadded boron, so that generation of the misfit dislocation can beeffectively restrained.

In the above Patent Document 2, since boron and germanium are added asdopants, the lattice constant that is changed under the influence of thehighly doped boron at a site near an interface with a thermally-oxidizedfilm of silicon wafer is compensated by germanium. Consequently, nostrain occurs on a wafer facial layer after the thermally oxidized filmis removed and the wafer is not deformed while growing the epitaxiallayer, so that no misfit dislocation occurs in the epitaxial layer.

On the other hand, Patent Document 3 discloses an exemplary use ofphosphorus (P) as an N-type dopant. According to the technique disclosedin Patent Document 3, germanium is added when a large amount ofphosphorus is doped in silicon to compensate for the strain in crystallattice caused by phosphorus to prevent the misfit dislocation frombeing generated.

[Patent Document 1] JP-A-2004-175658

[Patent Document 2] JP-A-2005-223092

[Patent Document 3] JP-A-09-7961

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

However, the technique disclosed in patent document 3 accompanies thefollowing problems.

Specifically, addition of a large amount of phosphorus and germanium asdopants as in the above, especially when an N-type low-resistivitycrystal is to be grown, results in excessively large freezing pointdepression to cause a compositional supercooling phenomenon.

When a large compositional supercooling occurs, a growth different fromthat at silicon growth face starts at a crystal growth interface, whichcauses an abnormal growth (Cell growth). When such an abnormal growthoccurs during an ingot-growing phase, monocrystallization is hindered.

An object of the invention is to provide a producing method of siliconmonocrystal that is adapted to produce an N-type highly dopedmonocrystal without causing abnormal growth within a crystal when asilicon monocrystal is to be grown by Czochralski (CZ) method, and anN-type highly doped semiconductor substrate.

Means for Solving the Problems

A producing method of a silicon monocrystal according to an aspect ofthe invention includes: adding phosphorus (P) and germanium (Ge) into asilicon melt or adding phosphorus into a silicon/germanium melt; andgrowing a silicon monocrystal from the silicon melt by a Czochralskimethod, in which a phosphorus concentration [P]_(L)(atoms/cm³) in thesilicon melt, a Ge concentration in the silicon monocrystal, an averagetemperature gradient G_(ave) (K/mm) and a pull speed V (mm/min) arecontrolled to satisfy a formula (1) as follows, the phosphorusconcentration [P](atoms/cm³) in the silicon monocrystal is 4.84×10¹⁹atoms/cm³ or more and 8.49×10¹⁹ atoms/cm³ or less, and the phosphorusconcentration [P](atoms/cm³) and the Ge concentration [Ge](atoms/cm³) inthe silicon monocrystal satisfy a relationship according to a formula(2) as follows while growing the silicon monocrystal.[P]_(L)+(0.3151×[Ge]+3.806×10¹⁸)/1.5<0.5×(G _(ave) /V+43)×10¹⁹  (1)[Ge]<−6.95×[P]+5.90×10²⁰  (2)

In the above, the concentration of germanium in the growing crystal isdifficult to be controlled because the concentration accords withtheoretical equilibrium segregation in accordance with a doping amount.Therefore, the phosphorus concentration is controlled by a pull-upcondition, mainly by pressure, flow volume of inert gas (Ar) in thechamber and pull-up speed as well as the doping amount to be adjusted toa desired level of concentration.

According to the above aspect of the invention, since the relationshipbetween the phosphorus concentration and the germanium concentration inthe growing crystal satisfies the relationship shown in the formula (2),a monocrystal can be grown without causing an abnormal growth in thecrystal, thus stably obtaining an N-type highly doped semiconductorsubstrate.

Further, when phosphorus and germanium are simultaneously doped, finalmonocrystallization rate after pulling up the crystal can be improvedand deformation of crystal during the pulling-up process at the initialstage of doping can be prevented.

A producing method of a silicon monocrystal according to another aspectof the invention includes: adding phosphorus (P) and germanium (Ge) intoa silicon melt or adding phosphorus into a silicon/germanium melt; andgrowing a silicon monocrystal from the silicon melt by a Czochralskimethod a phosphorus concentration, where a phosphorus concentration[P]_(L)(atoms/cm³) in the silicon melt, a Ge concentration in thesilicon monocrystal, an average temperature gradient G_(ave) (K/mm) anda pull speed V (mm/min) are controlled to satisfy a formula (3) asfollows, the phosphorus concentration [P](atoms/cm³) and the Geconcentration [Ge](atoms/cm³) in the silicon monocrystal satisfy arelationship according to a formula (4) as follows while growing thecrystal, where d_(Si)(Å) represents a lattice constant of silicon,r_(Si)(Å) represents a covalent radius of silicon, r_(P)(Å) represents acovalent radius of phosphorus and r_(Ge)(Å) represents a covalent radiusof Ge.

$\begin{matrix}{{\lbrack P\rbrack_{L} + {\left( {{0.3151 \times \lbrack{Ge}\rbrack} + {3.806 \times 10^{18}}} \right)/1.5}} < {0.5 \times \left( {{G_{ave}/V} + 43} \right) \times 10^{19}}} & (3) \\{{\left( {{\left( \frac{r_{Ge} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack{Ge}\rbrack}{\lbrack{Si}\rbrack}} + {\left( \frac{r_{p} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack P\rbrack}{\lbrack{Si}\rbrack}}} \right) \times d_{Si}} < {{{- 4.24736} \times 10^{- 23} \times \lbrack P\rbrack} + {2.78516 \times 10^{- 3}}}} & (4)\end{matrix}$

By thus growing the crystal while satisfying the relationship betweenthe phosphorus concentration and Ge concentration, an abnormal growthcan also be prevented while growing the crystal.

In the above aspect of the invention, the phosphorus concentration[P](atoms/cm³) and the Ge concentration [Ge](atoms/cm³) in the siliconmonocrystal preferably satisfy a relationship according to a formula (5)as follows while growing the crystal.2.2×[P]−8.62×10¹⁹<[Ge]<2.2×[P]+8.62×10¹⁹  (5)

According to the above arrangement, since a predetermined amount ofgermanium is doped, lattice distortion caused by phosphorus can bereliably compensated by germanium, so that generation of misfitdislocation can be avoided when epitaxial layer is formed on a surfaceof a semiconductor substrate obtained from a produced ingot.Incidentally, there is no lower limit in the germanium concentration interms of abnormal growth occurrence.

An N-type highly doped semiconductor substrate according to stillanother aspect of the invention is obtained by: adding phosphorus (P)and germanium (Ge) into a silicon melt or adding phosphorus into asilicon/germanium melt; and growing a silicon monocrystal from thesilicon melt by a Czochralski method, in which a phosphorusconcentration [P]_(L)(atoms/cm³) in the silicon melt, a Ge concentrationin the silicon monocrystal, an average temperature gradient G_(ave)(K/mm) and a pull speed V (mm/min) are controlled to satisfy a formula(6) as follows, the phosphorus concentration [P](atoms/cm³) in thesilicon monocrystal is 4.84×10¹⁹ atoms/cm³ or more and 8.49×10¹⁹atoms/cm³ or less, and the phosphorus concentration [P](atoms/cm³) andthe Ge concentration [Ge](atoms/cm³) in the silicon monocrystal satisfya relationship according to a formula (7) as follows while growing thesilicon monocrystal.[P]_(L)+(0.3151×[Ge]+3.806×10¹⁸)/1.5<0.5×(G _(ave) /V+43)×10¹⁹  (6)[Ge]<−6.95×[P]+5.90×10²⁰  (7)

An N-type highly doped semiconductor substrate according to a furtheraspect of the invention is obtained by: adding phosphorus (P) andgermanium (Ge) into a silicon melt or adding phosphorus into asilicon/germanium melt; and growing a silicon monocrystal from thesilicon melt by a Czochralski method, in which a phosphorusconcentration [P]_(L)(atoms/cm³) in the silicon melt, a Ge concentrationin the silicon monocrystal, an average temperature gradient G_(ave)(K/mm) and a pull speed V (mm/min) are controlled to satisfy a formula(8) as follows, the phosphorus concentration [P](atoms/cm³) and the Geconcentration [Ge](atoms/cm³) in the silicon monocrystal satisfy arelationship according to a formula (9) as follows while growing thesilicon monocrystal, where d_(Si)(Å) represents a lattice constant ofsilicon, r_(Si)(Å) represents a covalent radius of silicon, r_(P)(Å)represents a covalent radius of phosphorus and r_(Ge)(Å) represents acovalent radius of Ge.

$\begin{matrix}{{\lbrack P\rbrack_{L} + {\left( {{0.3151 \times \lbrack{Ge}\rbrack} + {3.806 \times 10^{18}}} \right)/1.5}} < {0.5 \times \left( {{G_{ave}/V} + 43} \right) \times 10^{19}}} & (8) \\{{\left( {{\left( \frac{r_{Ge} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack{Ge}\rbrack}{\lbrack{Si}\rbrack}} + {\left( \frac{r_{p} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack P\rbrack}{\lbrack{Si}\rbrack}}} \right) \times d_{Si}} < {{{- 4.24736} \times 10^{- 23} \times \lbrack P\rbrack} + {2.78516 \times 10^{- 3}}}} & (9)\end{matrix}$

In the above aspect of the invention, the phosphorus concentration[P](atoms/cm³) and the Ge concentration [Ge](atoms/cm³) in the siliconmonocrystal preferably satisfy the relationship according to a formula(10).2.2×[P]−8.62×10¹⁹<[Ge]<2.2×[P]+8.62×10¹⁹  (19)

In the above, a resistivity of the N-type highly doped semiconductorsubstrate is preferably 3 mΩ·cm or less.

The resistivity may be at any level in a range of 3 mΩ·cm or less,however, preferably in a range of 2.5 mΩ·cm or less and more preferablyin a range of 1.5 mΩ·cm or less. Incidentally, the resistivity of theN-type highly doped semiconductor substrate can be theoretically loweredby controlling an average temperature gradient Gave (k/mm) of thesilicon crystal near a surface of the silicon melt and a pulling-upspeed V (mm/min). However, considering practical productivity, areference lower limit is 0.5 mΩ·cm.

According to the above arrangement, since a low-resistive substrate canbe reliably produced by a stable producing method, the substrate can befavorably used as a substrate of a power MOSFET and the like.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a scatter diagram showing a relationship between asolidification rate and resistivity of a growing crystal in an exemplaryembodiment of the invention.

FIG. 2 is a graph showing a relationship between a phosphorusconcentration in a silicon melt and Gave/V in the above exemplaryembodiment.

FIG. 3 is a graph for converting a germanium concentration in thegrowing crystal into a phosphorus concentration in the above exemplaryembodiment.

FIG. 4 is a graph showing a relationship between a conversion dopantconcentration in which the germanium concentration is converted into thephosphorus concentration to be added and Gave/V in the above exemplaryembodiment.

FIG. 5 is a graph showing a relationship between a phosphorusconcentration and germanium concentration in the growing crystal in theabove exemplary embodiment.

FIG. 6 is a graph showing a relationship between a phosphorusconcentration in the growing crystal and difference in lattice constantin the above exemplary embodiment.

FIG. 7 is a graph showing a relationship between a phosphorusconcentration and germanium concentration in the growing crystal in theabove exemplary embodiment.

FIG. 8 is a graph showing a relationship between an elapsed time afterloading a dopant and a deformation frequency of a pulled-up crystal.

BEST MODE FOR CARRYING OUT THE INVENTION

An exemplary embodiment of the invention will be described below withreference to the attached drawings.

1. On Abnormal Growth

Initially, abnormal growths occurred when a monocrystal is grown by CZmethod from a silicon melt in which only phosphorus is doped and from asilicon melt in which phosphorus and germanium are co-doped are checked.Pull-up conditions at this time are shown in the following tables 1 and2, where a pull-up speed as well as a doping amount of germanium isaltered as a control parameter.

Incidentally, in order to co-dope phosphorus and germanium, thefollowing arrangement is employed.

Initially, a doping device having an upper dopant chamber and a lowerdopant chamber are provided, the upper and lower dopant chambersrespectively accommodating different dopants, an upper part of the upperdopant chamber being opened and a lower part of the lower dopant chamberbeing opened. Phosphorus is accommodated in the upper dopant chamber andgermanium is accommodated in the lower dopant chamber.

Next, the doping device is situated above a quartz crucible in whichsilicon melt is supplied. Subsequently, the doping device is placed neara position at which temperature is raised to a melting point ofphosphorus and germanium. Then, phosphorus is evaporated to be a dopantgas, which is flowed out of the upper opening of the upper dopantchamber and is guided toward a proximity of a surface of the siliconmelt to be dissipated into the silicon melt. On the other hand,germanium is liquefied to flow out of the lower opening of the lowerdopant chamber to be dissipated into the silicon melt through a conduit.

TABLE 1 No. 1 No. 2 No. 3 No. 4 No. 5 Charged Amount (kg) 100 100 100100 100 P-Doping Amount (g) 500 500 500 500 500 Ge-Doping Amount (g) 0750 750 500 500 Target Resistivity Rate 1.3 1.3 1.3 1.3 1.3 (mΩ · cm)Cylindrical Pull-Up Speed 0.75->0.4 0.75->0.4 0.75->0.3 0.75->0.250.75->0.2 Body (mm/min) Condition Pressure in Furnace 59985 59985 5998559985 59985 (Pa) Ar Flow Rate 200 200 200 200 200 (L/min)

TABLE 2 No. 6 No. 7 No. 8 No. 9 Charged Amount (kg) 100 100 100 100P-Doping Amount (g) 500 500 500 500 Ge-Doping Amount (g) 500 600 750 750Target Resistivity Rate 1.3 1.3 1.3 1.3 (mΩ · cm) Cylindrical Pull-UpSpeed 0.75->0.2 0.75->0.2 0.75->0.2 0.75->0.4 Body (mm/min) ConditionPressure in Furnace 59985 59985 59985 59985 (Pa) Ar Flow Rate 200 200200 200 (L/min)

After studying the relationship between the solidification rate andresistivity of the grown monocrystal, results shown in FIG. 1 wasobtained. Incidentally, the signs “OK” after the number of therespective pull-up conditions indicate that no abnormal growth occurredand the signs “NG” indicate that abnormal growths occurred.

In a sample No. 1 in which only phosphorus was doped, an abnormal growthoccurred in an area A1. In contrast, in samples Nos. 2 to 9 in whichphosphorus and germanium were co-doped, the abnormal growth occurred inan area A2, which showed that the abnormal growth occurred on ahigh-resistivity side as compared to the one in which only phosphoruswas doped. It is assumed that this resulted from the doping ofgermanium.

Next, in the sample No. 1 in which only phosphorus was doped, phosphorusconcentration in the silicon melt (melt concentration) was plotted alonga horizontal axis and a ratio between an average temperature gradientGave (K/mm) of the silicon crystal near the surface of the silicon meltand pull-up speed V (mm/min) was plotted along a vertical axis. Thestudy of a relationship between the concentration and the ratio revealedthat the abnormal growth occurred in an area A3 as shown in FIG. 2,where a critical line G1 that divided the area according to the presenceof the occurrence of the abnormal growth could be drawn.

In the above, the average temperature gradient Gave (K/mm) is defined asa variant representing heat-radiation properties of a silicon crystalnear the surface of the silicon melt in a CZ furnace, which is morespecifically defined in the following article:

“Prediction of solid-liquid interface shape during CZ Si crystal growthusing experimental and global simulation” (Journal of Crystal Growth,Volume 266, Issues 1-3, May 15, 2004, P. 28-33, by Yutaka Shiraishi,Susumu Maeda and Kozo Nakamura)

After calculating a formula representing the critical line G1 in FIG. 2,it was revealed that the ratio Gave/V (K·min/mm²) between the averagetemperature gradient Gave (K/mm) and the pull-up speed V(mm/min)followed the following formula (11) according to the phosphorusconcentration in the silicon melt [P] (atoms/cm³):G _(ave) /V=2.0×10⁻¹⁹[P]−43  (11)

Since no abnormal growth occurred in the area on the left side of thecritical line G1 in FIG. 2, it is recognized that the abnormal growthdoes not occur when the following formula (12) is satisfied.G _(ave) /V>2.0×10⁻¹⁹[P]−43  (12)

Next, a relationship between the critical line G1 and the occurrence ofthe abnormal growth in the samples Nos. 2 to 9 in which phosphorus andgermanium were co-doped was studied. Then, it was confirmed that theabnormal growth also occurred in an area on the left side given by theabove formula (11), i.e. on a lower-concentration side of the criticalline G1 in which only phosphorus was doped. It is considered that theabnormal growth occurred because the freezing point depression degree ofthe silicon melt was increased on account of the co-doped germanium.

Accordingly, the freezing point depression degrees according to alteringgermanium concentration in the silicon melt were calculated in asilicon-germanium phase diagram to calculate a phosphorus concentrationequivalent to the freezing point depression degree according togermanium concentration. In other words, it is supposed that, on thebasis of phosphorus concentration, the critical line G1 given by theabove formula (12) remained unchanged since the average temperaturegradients of the silicon crystal near the silicon melt were the same.

The relationship between the freezing point depression degree bygermanium and the phosphorus concentration in the crystal equivalent tothe germanium is disclosed in:

“PHYSICOCHEMICAL PRINCIPLE OF SEMICONDUCTOR DOPING”

(V. M. Glazov, V. S. Zemskov., P. 142-(1968)

which can be represented in a graph G3 shown in FIG. 3.

The formula giving the graph G3 can be represented by the followingformula (13), where a conversion concentration in which germaniumconcentration in a growing crystal is converted into phosphorusconcentration is [Ge→P]s (atoms/cm³) and germanium concentration in thegrowing crystal is [Ge]s (atoms/cm³).[Ge→P]_(S)=0.3151×[Ge]_(S)+3.806×10¹⁸  (13)

Since the abnormal growth is influenced by a dopant concentration in thesilicon melt, the following formula (14) is established by convertingthe above formula (13) into the concentration in the silicon meltaccording to theoretical expression of equilibrium segregationC_(S)=kC_(L) (k: coefficient of equilibrium segregation), where solidconcentration is C_(S) and concentration in the melt is C_(L).Incidentally, the conversion concentration in which germaniumconcentration in the silicon melt is converted into phosphorusconcentration is represented as [Ge→P]_(L) (atoms/cm³).[Ge→P]_(L)=(0.3151×[Ge]_(S)+3.806×10¹⁸)/k  (14)

Accordingly, when phosphorus and germanium are co-doped, the dopantconcentration in the silicon melt [X] can be calculated according to thefollowing formula (15). Incidentally, the conversion concentration inwhich germanium concentration in the silicon melt is converted intophosphorus concentration is represented as [Ge→P]_(L) (atoms/cm³) andthe phosphorus concentration in the silicon melt is [P]_(L)(atoms/cm³).[X]=[P]_(L)+[Ge→P]_(L)  (15)

However, when the dopant concentration [X] according to the aboveformula (15) was directly applied, it was found that the dopantconcentration was shifted off the area represented by the formula (12).Accordingly, in order to adjust the dopant concentration to the arearepresented by the formula (12), [Ge→P]_(L) was subjected to a fitting,where the dopant concentration [X] in the silicon melt was set as in thefollowing formula (16) with the use of a coefficient of 0.66 (1/1.5).[X]=[P]_(L)+[Ge→P]_(L)/1.5  (16)

When the relationship between the critical line G1 and the abnormalgrowth occurrence areas in the samples Nos. 2 to 9 was checked based onthe converted dopant concentration [X], it was found that, as shown inFIG. 4, the abnormal growth occurrence area A4 was shown on the rightside of the critical line G1, i.e. on the high-concentration side andthe abnormal growth occurrence area A4 was not shown on the left side ofthe critical line G1, i.e. on the low-concentration side.

In other words, it was confirmed that, when phosphorus and germaniumwere co-doped, the occurrence of the abnormal growth did not occuraccording to the above conversion in an area on the low-concentrationside relative to the critical line G1 given by the above formula (11).

In view of the above, the condition for preventing the generation of anabnormal growth in a growing crystal is given by the following formula(17), where phosphorus concentration [P], germanium concentration [Ge]and Gave/V in the silicon melt are used as parameters.[P]_(L)+(0.3151×[Ge]+3.806×10¹⁸)/1.5<0.5×(G _(ave) /V+43)×10¹⁹  (17)

The above test showed that, even when phosphorus and germanium wereco-doped, occurrence of an abnormal growth could be clearly determinedby a borderline of the critical line G1 that showed a border ofoccurrence of an abnormal growth when only phosphorus was doped.However, no physical explanation on how much germanium concentrationrelative to phosphorus concentration prevented the occurrence of theabnormal growth was given yet.

Accordingly, phosphorus concentration and germanium concentration in thegrown crystal according to the samples of Nos. 1 to 9 were compared in ascatter diagram. Then, a critical line G2 that divided anabnormal-growth occurring area and a non-occurring area was found asshown in FIG. 5. The critical line G2 is given by the following formula(18).[Ge]=−6.95×[P]+5.90×10²⁰  (18)

Since no abnormal growth occurred on the left side of the critical lineG2 given by the formula (18), the condition for avoiding the abnormalgrowth is given by the following formula (19).[Ge]<−6.95×[P]+5.90×10²⁰  (19)

Further, in order to conduct a pull-up operation so that the phosphorusconcentration [P] and germanium concentration [Ge] in the growingcrystal satisfy the formula (19), the doping amount of the respectivecomponents and the pull-up condition have to be controlled. Sincegermanium is not evaporated during the pull-up operation and thusaccords with theoretical equilibrium segregation, the germaniumconcentration incorporated into a crystal is determined by an initialinput. The concentration of phosphorus can also be controlled by aninitial input. However, the amount of phosphorus incorporated intocrystal does not accord with theoretical equilibrium segregation butdecreases on account of evaporation during the pull-up operation. Thus,the phosphorus concentration [P] can be controlled by controlling theevaporation.

Where, for instance, an evaporated amount of phosphorus from the siliconmelt doped with germanium is J: phosphorus concentration contained inthe silicon melt is N; flow volume of inert gas introduced into achamber during the pull-up operation is A; a pressure in the chamberduring the pull-up operation is Y; and coefficients are α and β, thephosphorus concentration can be controlled by controlling at least oneof the flow volume A and the pressure Y so that the evaporated amount Jbecomes a predetermined value at a predetermined timing during thepull-up operation based on the following formula (20), therebysatisfying the above formula (19).J=α√{square root over (X)}·exp(βN/√{square root over (Y)})  (20)

2. On Lattice Distortion

The scatter diagram shown in FIG. 5 can also be represented based onVegard's Law as a scatter diagram of phosphorus concentration[P](atoms/cm³) in the growing crystal and difference in lattice constantΔa(Δd_(Ge)+Δd_(P))(Å) representing a lattice distortion of silicon,which specifically is given as a scatter diagram shown in FIG. 6.

In FIG. 6, the plots in areas A5 and A6 represent samples in whichphosphorus and germanium were co-doped and the plots in an area A7represent samples in which only phosphorus was doped.

Circular plots represent that no abnormal growth occurred andrectangular plots represent that an abnormal growth occurred.

A critical line G3 that divides the area in accordance with theoccurrence of the abnormal growth can be drawn in the area A5 showingthe results of co-doping of phosphorus and germanium and the area A7showing the results of doping of only phosphorus. It is recognized thatno abnormal growth occurred on the left side of the critical line G3.

The critical line G3 is obtained based on experimental data, which iscalculated according to a difference in crystal lattice constantΔa(Å)=Δd_(Ge)+Δd_(P) (Δd_(Ge): strain of Si by Ge (Å), Δd_(P): strain ofSi by P (Å)). By growing a crystal so that the following formula (21) issatisfied, lattice distortion can be controlled while avoiding theabnormal growth by Vegard's Law. Incidentally, d_(Si)(Å) represents alattice constant of silicon, r_(Si)(Å) represents a covalent radius ofsilicon, r_(P)(Å) represents a covalent radius of phosphorus andr_(Ge)(Å) represents a covalent radius of Ge.

$\begin{matrix}{{\Delta\; a} = {{{\Delta\; d_{Ge}} + {\Delta\; d_{P}}} = {{\left( {{\left( \frac{r_{Ge} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack{Ge}\rbrack}{\lbrack{Si}\rbrack}} + {\left( \frac{r_{p} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack P\rbrack}{\lbrack{Si}\rbrack}}} \right) \times d_{Si}} < {{{- 4.24736} \times 10^{- 23} \times \lbrack P\rbrack} + {2.78516 \times 10^{- 3}}}}}} & (21)\end{matrix}$

The sample co-doping phosphorus and germanium exhibited a difference incrystal lattice constant Δa closer to zero as compared to the sample inwhich only phosphorus was doped, which shows that the lattice distortioncaused on account of phosphorus is mitigated by co-doping germanium.

Next, some of the grown crystals obtained according to pull-upconditions of Nos. 1 to 9 shown in Table 1 were sampled to compareoccurrences of misfit dislocation in providing an epitaxial layer onsemiconductor wafers cut from the grown crystal in which only phosphoruswas doped and on semiconductor wafers cut from the grown crystal inwhich phosphorus and germanium were co-doped.

The misfit dislocation was determined by photographing the surface ofthe semiconductor provided with the epitaxial layer by an X-raydiffraction measurement.

The results showing the occurrences of the misfit dislocations in thegrown crystal in which only phosphorus was doped are shown in Table 3.The results of the grown crystal in which phosphorus and germanium wereco-doped are shown in Table 4. Incidentally, “A” represents that “nomisfit dislocation occurred” and “B” represents that “misfit dislocationoccurred”.

TABLE 3 Resistivity (mΩ · cm) Epi Thickness 1 1.1 1.2 1.3 1.5 1.6 1.92.5 3.1 3.4 (μm) After Epi 15 B B B B B B B A A A 10 B B B B A B A A A A6 A A A A A A A A A A Thermal 15 B B B B B B B B B B treatment 10 B B BB B B B B A A after Epi 6 B B B B B B A A A A Difference in −7.75 −7.06−6.24 −5.61 −4.91 −4.54 −3.72 −2.84 −2.21 −1.95 Lattice constant (×10⁻⁴Å) Note P: 500 g

TABLE 4 Resistivity (mΩ · cm) Epi Thickness 1.01 1.16 1.36 1.16 1.39(μm) After Epi 15 A A A A A 10 A A A A A 6 A A A — — Thermal 15 B B B AA treatment 10 B B A A A after Epi 6 A A A A A Difference in −3.11 −3.71−3.25 −1.76 −1.95 Lattice constant (×10⁻⁴ Å) Note P: 500 g P: 500 g Ge:750 g Ge: 500 g

According to Table 3, when only phosphorus was doped, occurrence ofmisfit dislocation varied between a target resistivity 1.6 mΩ·cm and 1.9mΩ·cm. Thus, it can be recognized that misfit dislocation becomesdifficult to occur where the difference in lattice constant Δa relativeto silicon is approximately −4.0×10⁻⁴ Å.

Next, comparison between Tables 3 and 4 shows that, when only phosphoruswas doped, while the semiconductor wafer of target resistivity 1 mΩ·cmexhibited a difference in lattice constant of −7.75×10⁻⁴ Å, thesemiconductor wafer of target resistivity 1.01 mΩ·cm in which phosphorusand germanium were co-doped exhibited a difference in lattice constantof −3.11×10⁻⁴ Å. Accordingly, it is recognized that co-doping phosphorusand germanium greatly lessen the lattice distortion.

In view of the above, when phosphorus and germanium are to be co-doped,it is preferable that germanium doping amount relative to phosphorus inthe growing crystal is adjusted so that the difference in latticeconstant relative to silicon becomes −4.0×10⁻⁴ Å or less.

Specifically, phosphorus concentration [P](atoms/cm³) is fixed based onVegard's Law shown in the following formula (22) and germaniumconcentration [Ge](atoms/cm³) at which absolute value of the differencein lattice constant at the fixed phosphorus concentration is smallerthan ±4.0×10⁻⁴ Å is calculated. Incidentally, d_(Si) represents alattice constant (Å) of silicon.

$\begin{matrix}{{{\Delta\; d_{Ge}} + {\Delta\; d_{P}}} = {{{\pm 4.0} \times 10^{- 4}} = {\left( {{\left( \frac{r_{Ge} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack{Ge}\rbrack}{\lbrack{Si}\rbrack}} + {\left( \frac{r_{p} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack P\rbrack}{\lbrack{Si}\rbrack}}} \right) \times d_{Si}}}} & (22)\end{matrix}$

In sum, in order to restrain the misfit dislocation, it is preferablethat germanium concentration [Ge](atoms/cm3) relative to phosphorusconcentration [P](atoms/cm3) in a growing crystal is set within a rangespecified by the following formula (23).2.2×[P]−8.62×10¹⁹<[Ge]<2.2×[P]+8.62×10¹⁹  (23)

Based on the concentration range of germanium deduced by the formula(23) and the formula (19) defined in the above-mentioned “1. On AbnormalGrowth”, the germanium concentration range that restrains the misfitdislocation while avoiding abnormal growth in a certain phosphorusconcentration is the region surrounded by the abnormal-growth criticalline G2, and the misfit-restraining critical lines G4 and G5 accordingto the formula (23).

Further, a high-concentration N-type semiconductor substrate typicallyrefers to a substrate having 4.84×10¹⁹ atoms/cm³ or more of phosphorusconcentration. As shown in FIG. 7, since X intercept of the criticalline G2 is 8.49×10¹⁹ atoms/cm³, the concentration of phosphorus ispreferably set in a range represented by the following (24).4.84×10¹⁹≦[P]≦8.49×10¹⁹  (24)

3. Influence of Co-Doping of Phosphorus and Germanium

The above-described identification of the critical line G2 based on theabnormal growth and identification of the critical lines G4 and G5 inview of the lattice distortion generally apply to co-doping ofphosphorus and germanium, where germanium may be doped in the siliconmelt in advance and phosphorus may be subsequently doped as dopant gas.

In addition to the above, simultaneous doping of phosphorus andgermanium leads to the following unique advantages.

Specifically, in order to confirm the effect of the simultaneous dopingof phosphorus and germanium, comparison was made between a sampleobtained by initially doping germanium and subsequently pulling up whilesupplying phosphorus and another sample obtained by simultaneous doping.As a result, it was confirmed that final monocrystallization rate was88.0% in the germanium-initial doping, whereas the finalmonocrystallization rate was 92.6% in the simultaneous doping, whichproved, though slightly, that the monocrystallization rate was enhancedin the simultaneous doping.

Next, shoulder and sub-shoulder deformation of an ingot pulled-up afterthe germanium-initial doping and the simultaneous doping was examined.Then, as shown in FIG. 8, germanium-initial doping exhibited V-shapedincrease in the number of shoulder-deformation after approximately 10 to15 hours after loading the dopant. On the other hand, the simultaneousdoping exhibited gradual increase in the number of deformation inaccordance with the elapsed time after loading the dopant, where it wasconfirmed that the deformation did not occur at particular periods as inthe germanium-initial doping.

This is presumably because of the following reasons. When germanium isinitially doped, since the melting point of germanium is lower thansilicon, germanium is initially melted and silicon is melted thereafter,so that gas component is mingled when silicon melt and solid is mixedwith germanium melt to generate bubbles. Since germanium has a largesurface tension, once the bubbles are generated, the bubbles remains fora long time. Accordingly, even when germanium is totally dissolved intothe silicon melt, germanium adheres in growing a crystal, which inhibitsmonocrystallization.

On the other hand, since small portions of germanium are gradually mixedinto a large amount of silicon melt in the simultaneous doping, bubblesare unlikely to be generated.

The increase in the number of deformation in accordance with elapsedtime occurs presumably because of degradation of the quartz crucible ofthe pull-up device caused on account of long-time use, which isconsidered to influence also on the final monocrystallization rate.

Since the crystal has to be pulled up after a long time in thegermanium-initial doping because of the presence of the particularperiods at which the shoulder deformation is frequent. On the otherhand, no such particular periods are found in the simultaneous doping,so that the simultaneous doping greatly contributes to improvement inproductivity.

When a plurality of crystals are pulled up in the germanium-initialdoping, germanium concentration is decreased after pulling up the firstcrystal because of equilibrium segregation phenomenon. Accordingly, thedopant has to be supplemented. However, only phosphorus can be doped inthe germanium-initial doping, where originally desired properties forpreventing misfit dislocations cannot be given to the crystals.

On the other hand, since phosphorus and germanium are simultaneouslydoped in the simultaneous doping, silicon monocrystal with desiredproperties can be grown.

Further, after comparing the germanium concentration in a crystalrelative to germanium input, i.e. germanium absorption rate, in thegermanium-initial doping and that in the simultaneous doping, it wasfound that germanium absorption rate was only around 90% in thegermanium-initial doping, whereas the germanium absorption rate amountedto as high rate as 98% in the simultaneous doping.

Though not accurately known in detail, this is presumably becausespecific gravity of germanium is greater than silicon, so that germaniumis unequally resided in the lower part of the silicon melt in the quartzcrucible to cause the results.

The invention claimed is:
 1. A producing method of a siliconmonocrystal, comprising: adding phosphorus (P) and germanium (Ge) into asilicon melt or adding phosphorus into a silicon/germanium melt; andgrowing a silicon monocrystal from the silicon melt by a Czochralskimethod; wherein: a phosphorus concentration [P]_(L)(atoms/cm³) in thesilicon melt, a Ge concentration [Ge](atoms/cm³) in the siliconmonocrystal, an average temperature gradient G_(ave) (K/mm) and a pullspeed V (mm/min) are controlled to satisfy a formula (1) as follows; anda phosphorus concentration [P](atoms/cm³) and the Ge concentration[Ge](atoms/cm3) in the silicon monocrystal satisfy a relationshipaccording to a formula (2) as follows while growing the siliconmonocrystal, where d_(Si)(Å) represents a lattice constant of silicon,r_(Si)(Å) represents a covalent radius of silicon, r_(P)(Å) represents acovalent radius of phosphorus, and r_(Ge)(Å) represents a covalentradius of Ge: $\begin{matrix}{{\lbrack P\rbrack_{L} + {\left( {{0.3151 \times \lbrack{Ge}\rbrack} + {3.806 \times 10^{18}}} \right)/1.5}} < {0.5 \times \left( {{G_{ave}/V} + 43} \right) \times 10^{19}}} & (1) \\{{\left( {{\left( \frac{r_{Ge} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack{Ge}\rbrack}{\lbrack{Si}\rbrack}} + {\left( \frac{r_{p} - r_{Si}}{r_{Si}} \right) \times \frac{\lbrack P\rbrack}{\lbrack{Si}\rbrack}}} \right) \times d_{Si}} < {{{- 4.24736} \times 10^{- 23} \times \lbrack P\rbrack} + {2.78516 \times {10^{- 3}.}}}} & (2)\end{matrix}$
 2. The producing method according to claim 1, wherein thephosphorus concentration [P](atoms/cm³) and the Ge concentration[Ge](atoms/cm³) satisfy a relationship according to a formula (3) asfollows while growing the silicon monocrystal:2.2×[P]−8.62×10¹⁹<[Ge]<2.2×[P]+8.62×10¹⁹  (3).